{"title":"Integration Formulas Involving Fibonacci and Lucas Numbers","authors":"Kunle Adegoke, Robert Frontczak","doi":"arxiv-2406.00064","DOIUrl":null,"url":null,"abstract":"We present a range of difficult integration formulas involving Fibonacci and\nLucas numbers and trigonometric functions. These formulas are often expressed\nin terms of special functions like the dilogarithm and Clausen's function. We\nalso prove complements of integral identities of Dilcher (2000) and Stewart\n(2022). Many of our results are based on a fundamental lemma dealing with\ndifferentiation of complex-valued Fibonacci (Lucas) functions.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"31 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - General Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2406.00064","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We present a range of difficult integration formulas involving Fibonacci and
Lucas numbers and trigonometric functions. These formulas are often expressed
in terms of special functions like the dilogarithm and Clausen's function. We
also prove complements of integral identities of Dilcher (2000) and Stewart
(2022). Many of our results are based on a fundamental lemma dealing with
differentiation of complex-valued Fibonacci (Lucas) functions.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
